Cameron and Tyler Winklevoss, after abandoning an appeal to the U.S. Supreme Court, are still pursuing claims that Facebook Inc. founder Mark Zuckerberg stole the idea for the world's most popular social-networking site.

A day after the twin brothers from Greenwich said they won't ask the nation's high court to undo a 2008 settlement with Zuckerberg, they asked a federal judge in Boston on Thursday to let them determine whether Facebook hid instant messages that might have helped their case.

The Winklevoss twins said in the court filing they are seeking to find out whether Zuckerberg or Facebook "intentionally or inadvertently suppressed evidence."

Neel Chatterjee, a lawyer for Facebook, said in an email that "these are old and baseless allegations that have been considered and rejected previously by the courts."

The brothers were unsuccessful in federal trial and appeals courts in California in their effort to revoke the settlement of their claims in a 2004 lawsuit that Zuckerberg stole the idea for what became the world's most popular social network. They alleged that Palo Alto, Calif.-based Facebook didn't disclose an accurate valuation of its shares before they agreed to the $65 million cash and stock agreement.

Tyler Meade, a lawyer in Berkeley, Calif., representing the twins, said in Thursday's court filing that he's relying on a federal rule that allows judges to re-open litigation if important information wasn't produced. Meade asked a Boston judge to force the previous attorneys for the brothers to grant him access to certain documents, saying that they and Facebook's lawyers have refused to cooperate.